The figure shows the surface created when the cylinder&nbsp;y2+Z2=1&nbsp;intersects the cylinder&nbsp;x2+Z2=1. Find the area of this surface.The figure is below:

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The figure shows the surface created when the cylinder&amp;nbsp;y2+Z2=1&amp;nbsp;intersects the cylinder&amp;nbsp;x2+Z2=1. Find the area of this surface.The figure is below:

stuth1 · Accepted Answer

Note that the given cylinder will intersect at four congruent surfaces. e. equal in area. We need to find the area of only one side and then multiply it by 4.First, we find the area of the face of the surface that intersect the positive y axis. The surface is located above the area.&amp;nbsp;x2+z2=1&amp;nbsp;then&amp;nbsp;z=f(x,z)=1−z2&amp;nbsp;=∫∫x2+z2≤1fx2+fz2+1dA&amp;nbsp;=∫∫x2+z2≤1z21−z2+1dA&amp;nbsp;=∫−11∫−1−z21+z211−z2&amp;nbsp;dx&amp;nbsp;&amp;nbsp;dz&amp;nbsp;&amp;nbsp;=4∫01∫01−z211−z2&amp;nbsp;dx&amp;nbsp;&amp;nbsp;dz&amp;nbsp;&amp;nbsp;=limt→1+4∫0t∫01−z211−z2&amp;nbsp;dx&amp;nbsp;&amp;nbsp;dz&amp;nbsp;&amp;nbsp;=limt→1+4∫0t1&amp;nbsp;dt&amp;nbsp;&amp;nbsp;=4&amp;nbsp;Consequently, the sum of the areas of the intersecting surface is&amp;nbsp;4×4=16

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The figure shows the surface created when the cylinder y^2+Z^2=1 intersects the cylinder x^2+Z^2=1. Find the area of this surface.The figure is something like:FSP02510400011.jpgFSZ

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